TCB-spline-based isogeometric analysis method with high-qualityparameterizations
TCB-spline-based isogeometric analysis method with high-qualityparameterizations
复制标题
基于TCB样条的高质量参数化等几何分析方法
DOI：
10.1016/j.cma.2022.114771
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发表时间：
2022
影响因子：
7.2
通讯作者：
Yongjie Jessica Zhang
中科院分区：
文献类型：
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作者：
Zhihao Wang;Juan Cao;Xiaodong Wei;Yongjie Jessica Zhang
引入等几何分析（IGA），将分析方法和计算机辅助设计（CAD）集成为一个统一的过程。物理域的高质量参数化在IGA中起着至关重要的作用。然而，获得复杂几何形状的高质量参数化仍然是一个挑战。基于三角形结构的二元单纯样条（tcb样条）及其有理扩展在IGA环境中为经典非均匀有理b样条（NURBS）提供了一个有吸引力的替代方案，因为它们不仅与NURBS具有许多期望的特性，而且可以在一般多边形域上定义。在这项工作中，建议在IGA中使用tcb样条来克服NURBS张量积结构所带来的限制。我们提出了IGA在一般多边形域上使用有理tcb样条的方法。然后提出了一种根据给定的物理域边界生成参数域的方法。这使我们能够轻松地获得高质量的参数化，而无需诉诸优化方法。几个复杂物理域的数值算例证明了基于tcb样条的IGA方法的灵活性、高质量的参数化和数值解的准确性。
Isogeometric analysis (IGA) was introduced to integrate methods for analysis and computer-aided design (CAD) into a unified process. High-quality parameterization of a physical domain plays a crucial role in IGA. However, obtaining high-quality parameterizations for complex geometries retains a challenge. Triangle configuration based bivariate simplex splines (TCB-splines) and their rational extensions provide an attractive alternative to classical nonuniform rational B-splines (NURBS) in the context of IGA, as they not only share many desired properties with NURBS but also can be defined over general polygonal domains. In this work, using TCB-splines in IGA is suggested to overcome the limits posed by the tensor-product structure of NURBS. We present the methodology for IGA to use rational TCB-splines over general polygonal domains. Then a method to generate the parametric domain according to given physical domain boundaries is proposed. This allows us to obtain a high-quality parameterization easily without resorting to the optimization method. Several numerical examples with complex physical domains demonstrate the flexibility of our TCB-spline-based IGA method, the high quality of the parameterization, and the accuracy of the numerical solutions.